What is the primary purpose of a histogram?

Question

BlackTom AI · Accepted Answer

A histogram displays the distribution of a numerical variable by grouping (binning) values and plotting the frequency or density as adjacent bars.

1) Relevant knowledge points and concepts
- Histogram: a graphical summary for a single quantitative (numerical) variable. Values are divided into contiguous intervals (bins); bar heights show counts or relative frequencies.
- Purpose: reveal shape (symmetric, skewed), center, spread, modality (unimodal, bimodal), and potential outliers.
- Distinction from other plots: bar charts for categorical counts, scatterplots for relationships between two numerical variables, mosaic/contingency tables for relationships between categorical variables.

2) Step-by-step reasoning process
- Start with a list of numeric observations.
- Choose bin edges that partition the range into contiguous intervals.
- For each bin, count how many observations fall into that interval.
- Draw adjacent bars whose height equals each bin’s count (or proportion).
- Interpret the overall shape, peaks, gaps, and tails to describe the distribution.

3) Intermediate steps (construction example)
- Data: {2, 3, 3, 5, 7, 8, 8, 9}. Choose bins [2–4), [4–6), [6–8), [8–10).
- Counts: [2–4): 3 values (2,3,3); [4–6): 1 (5); [6–8): 1 (7); [8–10): 3 (8,8,9).
- Plot adjacent bars at heights 3, 1, 1, 3 to visualize distribution.

4) Why the correct answer is correct
- Option b precisely describes this process and purpose: histograms show how values of a numerical variable are distributed across ranges. They are designed to convey frequency/density across continuous or discrete numeric ranges.

5) Why other options are incorrect
- a. “To compare numerical and categorical variables” — comparing a numeric variable across categories is typically done with boxplots or grouped bar charts, not a single histogram.
- c. “Represent correlation between three numerical variables” — correlations and multivariate relationships require scatterplots, matrix plots, or 3D visualizations, not a histogram.
- d. “Visualise relationships between two categorical variables” — use contingency tables, stacked/bar charts or mosaic plots for two categorical variables.

6) Conclusion
- The correct choice is b. To show the distribution of a numerical variable. This matches the provided answer.

What is the primary purpose of a histogram?单项选择题

类似问题

In descriptive statistics, the mean is basically Blank ______.

Calculate the mean for the table below:

The following list gives the number of hours spent watching television in a week by a group of students: 15, 3, 25, 29, 10, 11, 0, 33.The mean and standard deviation are closest to:

What defines an outlier (IQR rule)?

What is the best way to measure precision?

A stock had returns of 5, 14, 11, -8, and 6 percent over the past 5 years. The standard deviation for this stock is:

When summarizing multiples (e.g., EV/EBITDA) across a set of comparable firms, analysts typically prefer the median over the mean because:

In the workshop example, it would be legitimate to draw attention to the large standard deviation in the data for butternut snap cookies and milk coffee biscuits, and to present potential explanations for the observed variation.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单